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Laurren LARROUY (GREDEG/CNRS, Université de Nice Sofia Antipolis) : Bayesian and relational rationality: from game theory to a theory of games

The object of the paper is to build a theory of games that does not require the existence of prior beliefs about each other’s actions. We indeed argue that the existence of prior beliefs about the outcome of a game is inconsistent with the rationality of individuals engaged in a strategic interaction. We suggest instead introducing a Theory of Mind (ToM) in game theory to explain how players choose their strategy given their beliefs about each others’ types. We ground our model on Simulation Theory (ST), and define as ‘relational rational’ a Bayesian rational player who chooses her strategy given her simulation of the reasoning of the other players.

Our contribution therefore questions the classical and the epistemic program in game theory that both fail to provide an intersubjective representation of strategic interactions. Classical game theorists are interested in the properties of a solution concept (e.g. existence, multiplicity, and stability), but without investigating how players could reach such a solution. Epistemic game theory (EGT) intends to determine the conditions on the knowledge and beliefs of the players such that their choices correspond to a specific solution concept. In other words, EGT is only testing the consistency of a solution to the game that is postulated before the actual playing of the game. Besides, much of the debate in EGT has focused on the nature of the prior beliefs (whether they are common or not, independent or not): our criticism goes further, by questioning the existence itself of prior beliefs about each other’s actions. Besides, the strategic dimension of games in both classical and epistemic game theory is captured by the assumption of common knowledge of rationality (CKR) – or, as a weaker requirement, of common belief in rationality. However as soon as it is supposed that each player is Bayes rational and that this is of common knowledge, there is no need to account for and endogenous formation of individual beliefs. In fact, a fundamental issue of game theory is that players never try to represent what the other players are thinking: they have an a priori belief about the result of their reasoning, but the process itself of the formation of those beliefs is never tackled.

To offer a proper theory of games, a mechanism is missing: this is a ToM. Introducing a ToM and in particular the ST in game theory offers a methodological ground to explain how players define their beliefs about each other’s actions. In brief, the ST states that individuals use their own mental scheme, to explain and predict others’ behavior by putting themselves in place of these others and by simulating, from this angle, others’ eventual perceptions, and beliefs. They implement in their own reasoning process others’ ‘pretend’ mental states to infer others’ potential actions. Such mechanism implies that the individuals’ prediction depend on their own perceptions or frames. This perspective makes possible to constrain the set of beliefs a player can hold and her simulation of others’ mental states – i.e. perceptions and beliefs.